Automorphism Groups of Homogeneous Semilinear Orders: Normal Subgroups and Commutators
Automorphism Groups of Homogeneous Semilinear Orders: Normal Subgroups and Commutators
复制标题
齐次半线性阶的自同构群：正规子群和交换子
DOI：
--
复制
发表时间：
1991
期刊：
影响因子：
--
通讯作者：
H. D. Macpherson
中科院分区：
文献类型：
--
作者：
M. Droste;W. Holland;H. D. Macpherson
一个偏序集（T，≤）称为树，如果它是半线性序的，即任何两个元素有一个公共下界，但没有两个不可比元素有一个公共上界，并且包含一个无限链和至少两个不可比元素。设k ∈ φ。我们称偏序集（T，≤）是k-齐次的，如果T的两个k元子集之间的每个同构扩张为（T，≤）的一个自同构;弱k-传递的，如果对T的任意两个k元子链，存在（T，≤）的一个互取自同构。
A partially ordered set (T, ≤) is called a tree if it is semilinearly ordered, i.e. any two elements have a common lower bound but no two incomparable elements have a common upper bound, and contains an infinite chain and at least two incomparable elements. Let k ∈ ℕ. We say that a partially ordered set (T, ≤) is k-homogeneous, if each isomorphism between two k-element subsets of T extends to an automorphism of (T, ≤), and weakly k-transitive, if for any two k-element subchains of T there exists an automorphism of (T, ≤) taking one to the other.